Solve the Inequality for y 5y+3>-7y+13

$5 y + 3 > - 7 y + 13$

Move all terms containing $y$ to the left side of the inequality.

Add $7 y$ to both sides of the inequality.

$5 y + 3 + 7 y > 13$

Add $5 y$ and $7 y$ .

$12 y + 3 > 13$

Move all terms not containing $y$ to the right side of the inequality.

Subtract $3$ from both sides of the inequality.

$12 y > 13 - 3$

Subtract $3$ from $13$ .

$12 y > 10$

Divide each term in $12 y > 10$ by $12$ and simplify.

Divide each term in $12 y > 10$ by $12$ .

$\frac{12 y}{12} > \frac{10}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 y}{12} > \frac{10}{12}$

Divide $y$ by $1$ .

$y > \frac{10}{12}$

Simplify the right side.

Cancel the common factor of $10$ and $12$ .

Factor $2$ out of $10$ .

$y > \frac{2 (5)}{12}$

Cancel the common factors.

Factor $2$ out of $12$ .

$y > \frac{2 \cdot 5}{2 \cdot 6}$

Cancel the common factor.

$y > \frac{2 \cdot 5}{2 \cdot 6}$

Rewrite the expression.

$y > \frac{5}{6}$

The result can be shown in multiple forms.

Inequality Form:

$y > \frac{5}{6}$

Interval Notation:

$(\frac{5}{6}, \infty)$